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Algorithmic Problems in Peptide
Sequencing
Outline


Basics of Proteomics

Roles and Anatomy of Proteins

Tandem Mass Spectrometry
Algorithms for Peptide Identifications

De Novo Sequencing

An Algorithm for Perfect Spectra

Peptide Identification in Real World

Discussions
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Briefings
• We mainly focus on the following result:
– Ting Chen, Ming-Yang Kao, Matthew Tepel, John Rush and
George Church, A Dynamic Programming Approach to
De Novo Peptide Sequencing via Tandem Mass
Spectrometry, Journal of Computational Biology, 8(3):
325-337, 2001.
– Its preliminary version also appears in The 11th Annual
SIAM-ACM Symposium on Discrete Algorithms (SODA
2000), page 389-398, 2000.
• One of the most-cited algorithm articles in the
computational proteomics community.
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Outline


Basics of Proteomics

Roles and Anatomy of Proteins

Tandem Mass Spectrometry
Algorithms for Peptide Identifications

De Novo Sequencing

An Algorithm for Perfect Spectra

An Improved Version

Peptide Identification in Real World

Discussions
De Novo Sequencing for Peptide Identificaiton
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Anatomy of Protein Molecules
• Residue (of the peptides)
• Neutral peptide
H
H
O
NH
C
C
OH
NH
Rx
H
O
C
C
Rx
Stable state in nature
Basic building blocks
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Proteins and Peptides
H2 N
H
O
C
C
146.19
128.17
R
174.13
156.11
N
H
R1
K
H
H
H
O
H
H
O
N
C
C
N
C
C
C
C
R2 O
R3
R4
H
H2 N
C
C
R1
C
H
R5
H
H
O
H
H
O
N
C
C
N
C
C
R3
O
N
COOH
trypsin + H2O
arginine (R)
or lysine (K)
H
H
R4
H
N
C
H
R5
COOH
H
N
H
C
C
OH
Rectangles stand for amino acid residues
R2
O
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Amino Acid Molecules
• Please visit http://www.ionsource.com/ for more
information.
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Outline


Basics of Proteomics

Roles and Anatomy of Proteins

Tandem Mass Spectrometry
Algorithms for Peptide Identifications

De Novo Sequencing

An Algorithm for Perfect Spectra

Peptide Identification in Real World

Discussions
De Novo Sequencing for Peptide Identificaiton
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Tandem Mass Spectrometry
• Mass Spectrometers measure the mass of charged ions.
– A mass spectrometer has 3 major components.
Sample
+
_
Ionizer
Mass Analyzer
Detector
Adapted from Nathan Edwards’ slides
De Novo Sequencing for Peptide Identificaiton
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Proteomics via Mass Spectrometers
Enzymatic Digest
and
Fractionation
First stage MS
MS/MS
Precursor selection
and dissociation
Adapted from Nathan Edwards’ slides
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Outline


Basics of Proteomics

Roles and Anatomy of Proteins

Tandem Mass Spectrometry
Algorithms for Peptide Identification

De Novo Sequencing

An Algorithm for Perfect Spectra

Peptide Identification in Real World

Discussions
De Novo Sequencing for Peptide Identificaiton
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Peptide Identification
• Given:
• A MS/MS spectrum (m/z, intensity, possibly along with its
retention time)
• The precursor mass
• Output:
• The amino-acid sequence of the peptide
• Imagine a deck of cards that you can cut many times
and obtains the sums of the upper or lower half
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Peptide Fragmentation Mechanism
N-Terminus
C-Terminus
b-ions
y-ions
y-ions
R
E
G
L
b-ions
L
G
E
De Novo Sequencing for Peptide Identificaiton
R
m/z
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Peaks in a Spectrum
• Peptide: L – G – E – R
Weight
Ion
Amino
Amino
Acids
Acids
114.2
b1
L
171.2
b2
LG
300.3
b3
LGE
Ion
Weight
GER y3
361.3
ER y2
304.3
R y1
175.2
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Manual De Novo Sequencing
667.27-536.24=131.03
Molecular weight of
M
128.09 ≈147.11-19
Molecular weight of
K
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Outline


Basics of Proteomics

Roles and Anatomy of Proteins

Tandem Mass Spectrometry
Algorithms for Peptide Identification

De Novo Sequencing

An Algorithm for Perfect Spectra

Peptide Identification in Real World

Discussions
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De Novo Sequencing
•
De Novo: From the beginning in Latin.
– Database search tools match against known
peptides.
•
Problem Definitions:
Given a spectrum ( a set of real intervals ),
a mass value M,
compute a sequence P, ( a set of real number with specific order)
s.t. m(P)=M, and the matching score is maximized.
m(P) is the sum of residue mass.
M
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De Novo Sequencing: An Ideal Case
• An ideal tandem mass spectrum is noise-free and
contains only b- and y-ions, and every mass peak has
the same height.


The task is to find paths connecting two endpoints on a
directed acyclic graph.
The problem is : how to construct the ion ladder?
M
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Ion Ladders in an Ideal Case


Based on an ideal ion ladder, we can determine the
sequence by concatenating prefixes (or suffixes) in
order.
However, we cannot determine the ion type of a peak
before identifying it.
R
L
y1 E
G
y2 G
E
y3
Given only
L+ , ER+,
LGE+, R+
L
R
De Novo Sequencing for Peptide Identificaiton
m/z
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NC-Spectrum Model
•
We generate a (superset of ) ladder of ions.
– A Trick: Even if we cannot determine the ion types, we know
that an ion is either b-ion or y-ion.
1. Assume that we want to generate b-ion ladder.
2. If a peak is a b-ion, add the peak value to the list.
3. If a peak is a y-ion, add the complementary b-ion value to
the list.
•
This phase doubles the number of peaks.
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NC-Spectrum Model
• For the peptide sequence LGRE, we construct all
possible b-ions with respect to current spectrum.
• {P1, Q3, P4} or {P2, P3, Q1} are both complete ladders.
GER
LG
Q2
Q4 Q3
0
Q1
Pi: observed peaks
Qi: artificial peaks
m
m/2
P1
P2
P3 P4
L
R
ER LGE
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NC-Spectrum Model
•
Given a peak list = {P1,P2,P3, … , Pk}
•
The coordinates of all points along the line:
•
1. Pk – 1
Since the ion loses a Hydrogen
2. Qk = M – Pk+1 (why?)
(M – (Pk – 1 ) ) - 1
We still have to add two endpoints:
1. 0
2. M – 18
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NC Spectrum Model: A Summary
•
We are given k peaks.
– Now we have at most 2k+2 vertices.
•
Two vertices are adjacent if their coordinates differ by
the weight of some amino acid.
– The spectrum graph can be constructed in O(n2). (Why?)
•
The de novo sequencing is to search a path (or paths)
representing a good path from coordinate 0 to M-18.
– Such a path is not necessarily an ion ladder, though.
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Dynamic Programming Strategy
Dynamic Programming can solve this problem
efficiently.
•
–
Uni-directional (forward) DP does not work since it could
produce a solution containing both candidates for each
peak.
Q2
Q4 Q3
0
Q1
m
m/2
P1
P2
P3
De Novo Sequencing for Peptide Identificaiton
P4
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Dynamic Programming Strategy (Cont’d)
Dynamic Programming can solve this problem
efficiently using a different encoding scheme.
•
–
We approach the middle part from both end sides.
Q2
Q4 Q3
0
Q1
m
m/2
P1
P2
P3
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P4
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Dynamic Programming Strategy (Cont’d)
• Mass(b-ion) + Mass(y-ion) = PrecursorMass +2
– These b-ion candidates are nested pairs in the spectrum
graph.
0
m/2
De Novo Sequencing for Peptide Identificaiton
m
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Relabeling the Vertices
•
To encode the spectrum graph by the nested pairs, we
need to relabel the vertex number.
1. {0 = x0, x1, x2, …, xk, yk, …, y2, y1, y0 = m}
2. xi and yi are both generated from the same peak.
3. We go one level further in each iteration.
0
m/2
x0
xk
yk
De Novo Sequencing for Peptide Identificaiton
m
y0
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How Dynamic Programming Works
We design the |V|×|V| matrix M for representing
partial path candidates.
•
1.
M(i, j) = 1 iff [xo, xi] and [yj, yo] can occur simultaneouly in a legal
path.
2. For 1≦ s ≦ i, 1 ≦ s ≦ j, s occurs exactly once in the determined
partial path.
?
0
xi
yj
m/2
De Novo Sequencing for Peptide Identificaiton
m
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How Dynamic Programming Works
(Cont’d)
x0
x1
x2
x3
x4
y4
y3
y2
y1
y0
m/2
m
0
M(0,0) = 1
x0
M(0,1) = 1
x0
M(1,0) = 1
x0
y0
y1
x1
De Novo Sequencing for Peptide Identificaiton
y0
y0
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How Dynamic Programming Works
(Cont’d)
x0
x1
x2
x3
x4
y4
y3
y2
y1
y0
m/2
m
0
M(0,1) = 1
x0
M(1,0) = 1
x0
M(2,0) = 0
x0
y1
x1
x1
y0
y0
x2
y0
•M(1,0) =1 , but we cannot reach x2 from x0 nor x1.
M(2,1) = 1
x0
x2
y1
y0
•M(0,1) =1 , and we can reach x2 from x0.
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How Dynamic Programming Works
(Cont’d)
x0
x1
x2
x3
x4
y4
y3
y2
y1
y0
m/2
m
0
M(0,1) = 1
x0
M(1,0) = 1
x0
M(0,2) = 0
y1
x1
x0
y0
y0
y2
y1
y0
•M(0,1) =1 , but we cannot reach y2 from y0 nor y1.
M(1, 2) = 1
x0
x1
y2
y0
•M(1,0) =1 , and we can reach y2 from y0.
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Dynamic Programming: Preview
• In the i-th iteration, we determine and record all
possible (partial) paths in [0, xi] and [ yi, m].
0
m
m/2
x0
x0
…
xi-1
yt
xi or yi?
…
xi-1
xi
t < i-1
yi
De Novo Sequencing for Peptide Identificaiton
yt
…
…
y0
y0
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Dynamic Programming: Preview(Cont’d)
Path extension
• How can we reach yi?
• To calculate M(xj, yi) for all j < i,
• For every j < i, check if yi is adjacent to yt and M(xj, yt)
= 1, for some t < i
x0
…
xj
yi
yt
…
y0
– Then M(xj, yi) = 1. Otherwise, it is 0.
x0
…
xj
yi
De Novo Sequencing for Peptide Identificaiton
yt
…
y0
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Dynamic Programming: Preview(Cont’d)
Path extension
• Similarly, how can we reach xi?
• To calculate M(xi, yj) for all j < i,
• For every j < i, check if xi is adjacent to xt and M(xt, yj)
= 1, for some t < i
x0
…
xt
xi
yj
…
y0
– Then define M(xi, yj) =1.
x0
…
xt
xi
De Novo Sequencing for Peptide Identificaiton
yj
…
y0
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Dynamic Programming
m/2
m
0
x0
x1
x2
x3
x4
y4
M
y3
y0
y2
y1
y1
y2
y3
y0
y4
x0
x1
x2
x3
x4
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Dynamic Programming: Initialization
m/2
m
0
x0
x1
x2
x3
x4
y4
y3
M
y0
x0
1
y2
y1
y0
y1
y2
y3
y4
x1
0
0
0
0
x2
0
0
0
0
x3
0
0
0
0
x4
0
0
0
0
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Dynamic Programming: 1st iteraton
We then compute M(1,0) and M(0,1).
m/2
m
0
x0
x1
x2
x3
x4
Check the arcs (x0, x1) and
(y1, y0)
y4
y3
y2
M
y0
y1
x0
1
1
x1
1
y1
y0
y2
y3
y4
0
0
0
0
x2
0
0
0
0
x3
0
0
0
0
x4
0
0
0
0
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Dynamic Programming: Recursion (a)
For j = 2 to k
For i = 0 to j-2
(a) If M(i, j-1) = 1 and edge(Xi, Xj) = 1, then M(j, j-1) = 1.
m/2
m
0
x0
x1
x2
x3
x4
y4
y3
y1
M
y0
y1
x0
1
1
x1
1
0
y0
y2
y3
y4
0
0
0
x3
0
0
0
x4
0
0
0
x2
Can we adjust the leftmost endpoint to xj?
y2
De Novo Sequencing for Peptide Identificaiton
1
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Dynamic Programming: Recursion (b)
For j = 2 to k
For i = 0 to j-2
(b) If M(i, j-1) = 1 and edge(Yj, Yj-1) = 1, then M(i, j) = 1.
m/2
m
0
x0
x1
x2
x3
x4
y4
y3
y1
M
y0
y1
y2
x0
1
1
0
x1
1
0
y0
y3
y4
0
0
0
x3
0
0
0
x4
0
0
0
x2
Can we adjust the rightmost endpoint to yj?
y2
De Novo Sequencing for Peptide Identificaiton
1
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Dynamic Programming: Recursion (c)
For j = 2 to k
For i = 0 to j-2
(c) If M(j-1,i) = 1 and edge(Xj-1, Xj) = 1, then M(j, i) = 1.
m/2
m
0
x0
x1
x2
x3
x4
y4
Can we adjust the leftmost endpoint to xj?
y3
y2
y1
M
y0
y1
y2
x0
1
1
0
x1
1
0
x2
0
1
y0
y3
y4
0
0
0
x3
0
0
0
x4
0
0
0
De Novo Sequencing for Peptide Identificaiton
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Dynamic Programming: Recursion (d)
For j = 2 to k
For i = 0 to j-2
(d) If M(j-1, i) = 1 and edge(Yi, Yj) = 1, then M(j-1, j) = 1.
m/2
m
0
x0
x1
x2
x3
x4
y4
Can we adjust the rightmost endpoint to yj?
y3
y2
y1
M
y0
y1
y2
x0
1
1
0
x1
1
0
1
x2
0
1
y0
y3
y4
0
0
0
x3
0
0
0
x4
0
0
0
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Dynamic Programming (Cont’d)
Now for j = 3
m/2
m
0
x0
x1
x2
x3
x4
y4
y3
y2
y1
y0
M
y0
y1
y2
y3
x0
1
1
0
0
x1
1
0
1
1
x2
0
1
0
1
0
x3
0
0
1
0
0
0
0
0
x4
De Novo Sequencing for Peptide Identificaiton
y4
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Dynamic Programming (Cont’d)
Now for j = 4
m/2
m
0
x0
x1
x2
x3
x4
y4
y3
y2
y1
y0
M
y0
y1
y2
y3
y4
x0
1
1
0
0
0
x1
1
0
1
1
0
x2
0
1
0
1
0
x3
0
0
1
0
0
x4
0
0
0
1
0
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Dynamic Programming: Constructing the
Answer
• Legal path: Starting our search from the outermost regions ( the last
row/column):
– [x4, y4] -> [x3, y3] -> [x2, y2] ->[x1, y1]
– We backtrack M to search each edge corresponding to the feasible solution
m/2
m
0
x0
x1
x2
x3
x4
y4
y3
y2
y1
y0
M
y0
y1
y2
y3
y4
x0
1
1
0
0
0
x1
1
0
1
1
0
x2
0
1
0
1
0
x3
0
0
1
0
0
x4
0
0
0
1
0
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Dynamic Programming: Review
• Chen et al. create a new NC-specturm graph G=(V, E),
where V=2k+2 and k is the number of mass peaks
(ions).
• Given the NC-spectrum graph, we can solve the ideal
de novo peptide sequencing problem in O(|V|2) time
and O(|V|2) space.
– M construction : O(|V|2) time
– Constructing a feasible solution : O(|V|) time
• Therefore we find a feasible solution in O(|V|2) time
and O(|V|2) space.
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Outline


Basics of Proteomics

Roles and Anatomy of Proteins

Tandem Mass Spectrometry
Algorithms for Peptide Identification

De Novo Sequencing

An Algorithm for Perfect Spectra

Peptide Identification in Real World

Discussions
De Novo Sequencing for Peptide Identificaiton
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Noises in Real Spectra
•
The de novo strategy is too fragile to handle frequent
errors.
1. False negative peaks
•
Missing ions will break the path. The algorithms may find wrong
paths by concatenating two partial paths.
2. False positive peaks
•
The main critique of de novo strategy
3. Peak value is not the ion mass
•
Peak values represent the mass over charge value of ions.
•
It relies on the vendor. (Applied Biosystem)
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False Positives in Real Spectra
•
Different types of ions
– a-x, b-y, c-z
– Internal fragments/immonium ions
•
Neutral losses
– Neutral loss of water (~18Da)
– Neutral loss of ammonia (~17Da)
•
PTM (like adding new letters)
– Phosphorylation, glycopeptides
•
•
Isotopes
Unpurified samples
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Database Search Tools
• MASCOT: http://www.matrixscience.com/
• The de facto identification tool
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Database Search Tools (Cont’d)
• Brian Searle of Proteome Software informs us:
De Novo Sequencing for Peptide Identificaiton
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Peptide and Protein Identification
• A brief comparison of popular tools
Scoring Strategy
Representatives
Correlation, Z-score, posterior
probabilities
SEQUEST, MS-Tag, Scope, CIDentify, Popitam,
ProbID, and PepSearch
Statistical significance: E-values or Pvalues
Mascot, Sonar, InsPecT,
OMSSA, and X!Tandem
De Novo Sequencing
Pseudo-peaks
PEAKS
Spectrum graphs
Lutefisk, PepNovo, AUDENS
Statistical models
NovoHMM
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Outline


Basics of Proteomics

Roles and Anatomy of Proteins

Tandem Mass Spectrometry
Algorithms for Peptide Identification

De Novo Sequencing

An Algorithm for Perfect Spectra

An Improved Version

Peptide Identification in Real World

Discussions
De Novo Sequencing for Peptide Identificaiton
52/54
Wrap Up
• The MS/MS measures the mass of fragment ions.
– A single stage MS measures a collection of peptide.
• We generate ion ladders to reconstruct peptide
sequence.
– Masses are more reliable than intensities.
• De novo sequencing is an elegant strategy, but not
robust.
– We need some signal preprocessing strategies.
• Database search tools cannot handle novel proteins,
and results from different tools are often inconsistent.
– Integration of the two above methods may be a possible way.
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Some Guys You May Wish to Know
Affiliation Principal Investigators
Topics
ETH at Zurich
Ruedi Aebersold
Peptide-atlas, statistical significance
estimation
UCSD
Pavel Pevzner, Vineet Bafna
De novo sequencing: Multi-spectra
alignment
Waterloo
Bin Ma
De novo sequencing: SPIDER,
PEAKS
NIH
Yi-Kuo Yu
Signal calibration, statistical
significance estimation
Xerox
Andrew Goldberg, Marshall Bern
PTM
Georgetown
Nathan Edwards
Peptide identification
USC
Tim Chen
De Novo Sequencing
De Novo Sequencing for Peptide Identificaiton
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